how are games rendered in real-time gameplay?
The game engine uses openGL to render the image on screen. This is the same technology used to draw everything in blender's window. While video cards are designed to accelerate time consuming parts of openGL it is still common to keep the vertex count as low as possible to allow updating the window enough to get smooth animation. GLSL shading (that's openGL Shading Language) is also often used to get nicer results.

Maps is a fairly general term that is used in reference to the texturing used in the game engine. There are UVMaps that 'map' a location on a 3D model to a location on a 2d image. You can use several images on a finished model that are often referred to as maps. A normal map is an image containing details defining the 'surface distortion' this gives the appearance of detail that can cast shadows and highlights on the model without the extra geometry. A bump map is a simplified method of normal mapping. A specular map is an image that defines what parts of the model are shiny. Similarly a diffuse or texture map defines what diffuse colour is used at each part of the model.

Normally detailed models are created and then the detail is 'baked' onto these different 'maps' to be used during game play on a low poly model. This lets you do all the costly calculations at development time to give the game engine less work rendering the screen.

For the most part the texture options available when using the blender internal render engine are available when using the game engine. You can see the differences when you switch between the two, such as limited transparency, no mirror or subsurface scattering when using the game engine.